Theorems · Definition · algebraic topology
Path.Homotopic.setoid
{X : Type u} → [inst : TopologicalSpace X] → (x₀ x₁ : X) → Setoid (Path x₀ x₁)The setoid on Paths defined by the equivalence relation Path.Homotopic. That is, two paths are
equivalent if there is a Homotopy between them.
- Defined in
- Mathlib.Topology.Homotopy.Path
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Pathstatement · cited by 318
- Path.Homotopicproof · cited by 28
- Path.Homotopic.equivalenceproof · cited by 0
Cited by19
Results whose statement or proof uses this declaration.
- Path.Homotopic.Quotientproof · cited by 55
- IsCoveringMap.liftPathQuotientproof · cited by 3
- Path.Homotopic.pi_liftproof · cited by 3
- ContinuousMap.Homotopy.eq_path_of_eq_imagestatement and proof · cited by 2
- Path.Homotopic.hpath_hextstatement and proof · cited by 2
- unitInterval.uhpath01proof · cited by 2
- ContinuousMap.Homotopy.evalAt_eqstatement and proof · cited by 1
- ContinuousMap.Homotopy.heq_path_of_eq_imagestatement · cited by 1
- SimplyConnectedSpace.paths_homotopicproof · cited by 1
- IsQuotientCoveringMap.fundamentalGroupToMulOpposite_surjectiveproof · cited by 1
- simply_connected_iff_loops_nullhomotopicproof · cited by 1
- simply_connected_iff_paths_homotopicproof · cited by 1